Home
Class 12
MATHS
The perimeter of a triangle ABC right an...

The perimeter of a triangle ABC right angled at C is 70 and the inradius is 6, then `|a-b|=`

A

1

B

2

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
We know `Delta =sr=(70//2)xx6=210`
`rArr (1//2)ab=210rArr ab=420`
Now `(a+b)^(2)=(70-c)^(2)`
`rArr a^(2)+b^(2)+2ab=4900-140c + c^(2)`
`rArr c=(4900-2xx420)/(140)=29 " " [because a^(2)+b^(2)=c^(2)]`
`rArr (a-b)^(2)=a^(2)+b^(2)-2ab=c^(2)-2ab=841-840=1`
Promotional Banner

Topper's Solved these Questions

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|3 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The perimeter of a triangles ABC 6 times the arithemetic mean of the sine ratios of its angles if a =1 , A=

The perimeter of a triangle ABC is six times the arithmetic mean of the sines of its angles. If the side a is 1 then find angle Adot

The distance of incentre of the right-angled triangle ABC (right angled at A) from B and C are sqrt10 and sqrt5 , respectively. The perimeter of the triangle is _____

In a right triangle ABC, right angled at B, if tan A=1, then verify that 2sinAcosA=1.

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C

Draw and locate the centroid of the triangle ABC where right angle at A, AB = 8 cm and AC = 6 cm.

In a right angle triangle ABC with right angle at B , in which a= 24 units , b = 25 units and angle BAC =theta , then find sin A tan A ( A lt 90 ^(@))

CENGAGE-SOLUTIONS AND PROPERTIES OF TRIANGLE -SINGLE CORRECT ANSWER TYPE
  1. In a triangle ABC if tan.(A)/(2)tan.(B)/(2)=(1)/(3) and ab = 4, then t...

    Text Solution

    |

  2. In a triangle ABC if cot(A/2)cot(B/2)=c, cot(B/2)cot(C/2)=a and cot(C...

    Text Solution

    |

  3. The perimeter of a triangle ABC right angled at C is 70 and the inradi...

    Text Solution

    |

  4. The diagonals of a parallelogram are inclined to each other at an angl...

    Text Solution

    |

  5. In a triangle ABC if 2Delta^(2)=(a^(2)b^(2)c^(2))/(a^(2)+b^(2)+c^(2)),...

    Text Solution

    |

  6. If in any triangle, the area DeltaABC le(b^(2)+c^(2))/(lambda), then t...

    Text Solution

    |

  7. In any triangle ABC, if 2Delta a-b^(2)c=c^(3), (where Delta is the are...

    Text Solution

    |

  8. In A B C , show that a^2(s-a)+b^2(s-b)+c^(2)(s-c))=4R (1+r sin (A/2)s...

    Text Solution

    |

  9. Let ABC be an equilateral triangle, let KLMN be a rectangle with K...

    Text Solution

    |

  10. ABC is an acute angled triangle with circumcenter O and orthocentre H....

    Text Solution

    |

  11. In a triangle ABC if angle ABC=60^(@), then ((AB-BC+CA)/(r ))^(2)=

    Text Solution

    |

  12. The area of an acute triangle ABC is Delta, the area of its pedal tria...

    Text Solution

    |

  13. In a triangle ABC, D is a point on BC such that AD is the internal bis...

    Text Solution

    |

  14. In Delta ABC, circumrdius is 3 inradius is 1.5 units. The value of a a...

    Text Solution

    |

  15. AD, BE, CF are internal angular bisectors of Delta ABC and I is the in...

    Text Solution

    |

  16. In Delta ABC it is given distance between the circumcentre (O) and ort...

    Text Solution

    |

  17. In any Delta ABC line joiningcircumcentre (O) and incentre (I) is para...

    Text Solution

    |

  18. Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and...

    Text Solution

    |

  19. Let H be the orthocentre of triangle ABC. Then angle subtended by side...

    Text Solution

    |

  20. If in a triangle ABC, r(1)+r(2)+r(3)=9r, then the triangle is necessar...

    Text Solution

    |